Step 
Hyp 
Ref 
Expression 
1 

stoic4b.1 
$${\u22a2}\left({\phi}\wedge {\psi}\right)\to {\chi}$$ 
2 

stoic4b.2 
$${\u22a2}\left(\left({\chi}\wedge {\phi}\wedge {\psi}\right)\wedge {\theta}\right)\to {\tau}$$ 
3 
1

3adant3 
$${\u22a2}\left({\phi}\wedge {\psi}\wedge {\theta}\right)\to {\chi}$$ 
4 

simp1 
$${\u22a2}\left({\phi}\wedge {\psi}\wedge {\theta}\right)\to {\phi}$$ 
5 

simp2 
$${\u22a2}\left({\phi}\wedge {\psi}\wedge {\theta}\right)\to {\psi}$$ 
6 

simp3 
$${\u22a2}\left({\phi}\wedge {\psi}\wedge {\theta}\right)\to {\theta}$$ 
7 
3 4 5 6 2

syl31anc 
$${\u22a2}\left({\phi}\wedge {\psi}\wedge {\theta}\right)\to {\tau}$$ 